In this paper four boundary value problems for nonlinear ordinary differential equations are introduced: 1. Emden-Fowler problem in astrophysics, 2. Thomas-Fermi problem in atomic physics, 3. Blasius problem in fluid mechanics, 4. Bending of the beam. Firstly, for each problem there is a short physical explanation without any detailed mathematical derivation. Then the plots of approximate solutions are obtained by computer using the program Mathematica.